The Ridge Function Representation of Polynomials and an Application to Neural Networks

The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials, and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous functions, the rate of approximation obtained b...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2011-11, Vol.27 (11), p.2169-2176
Main Authors: Xie, Ting Fan, Cao, Fei Long
Format: Article
Language:English
Subjects:
Algebra
Approximation
Mathematical analysis
Mathematics
Mathematics and Statistics
Multivariate analysis
Neural networks
Polynomials
Representations
Ridges
Studies
代数多项式
多元多项式
多项式函数
应用
神经网络
表示法
连续函数
逼近问题
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Summary:The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials, and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous functions, the rate of approximation obtained by a neural network with one hidden layer is no slower than that of an algebraic polynomial.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-9407-1